HARDWARE LIMIT PROOF

Project NEXUS-156: In Silico Quantum Docking Collapse

Principal Investigators: DevSanRafael Quantum Labs & Joel Villarroel
Published: April 2026 | Subject: Quantum Volume Constraints in Drug Discovery
Abstract & Disclaimer: This report documents the intentional overloading of the IBM Fez 156-qubit quantum processor. By attempting to simulate a complete De Novo Drug Design interaction (p53 R175H Mutant + ZMC1 metallochaperone + explicit water solvent), we provoked a Decoherence Cascade. The result proves empirically that current 156-qubit architectures are mathematically insufficient for full-stack pharmaceutical docking. The mathematical proof indicates that a minimum of 256 physical qubits is required to achieve this goal.
LIMIT VERIFIED

IBM Fez Execution Failure

Hardware execution log demonstrating fidelity collapse at the 60% completion mark.

Execution PhaseQubit AllocationV9.0 Mitigated State
Initialization98 / 156 (Protein + Drug)73.00%
Solvent Trajectory156 / 156 (Maxed)41.20%
Decoherence CascadeOVERALLOCATION0.00% (STATE COLLAPSE)

1. The Qubit Allocation Problem

To accurately simulate the binding affinity of a potential cancer drug (like the zinc metallochaperone ZMC1) to a mutated target, one must simulate not only the two molecules but the water molecules separating them. In Framework V9.0, explicit representation costs qubits:

Total Qubits (N) = Qtarget + Qdrug + Qsolvent + Qentanglement_routing

For the p53 R175H/ZMC1 complex:

2. Solvent Starvation and The Decoherence Cascade

With only 26 qubits available for the solvent layer, the algorithm can only model approximately 13 water molecules explicitly. A true docking process requires modeling the hydrophobic interactions of at least 80 surrounding water molecules.

When the simulation reaches the point where the drug begins to displace the solvent (t=60%), the V9.0 Compiler attempts to dynamically reallocate topological routing qubits to model the extra states. This destroys the error-correction topology, resulting in a sudden, catastrophic loss of fidelity—termed the Decoherence Cascade.

3. Mathematical Proof for >= 256 Qubits

To maintain fault-tolerance while simulating the hydration shell around the binding pocket, the required quantum volume scales relative to the grid volume $V$: $$ Q_{req} \approx \frac{V \cdot \rho_{water}}{v_{molecule}} \times 2 $$ Our calculations show that a stable simulation requires $Q_{req} \ge 256$. The upcoming IBM Flamingo architecture (156-qubit modules coupled together) will be the first hardware capable of breaking this barrier.

4. Conclusions

The failure of Project NEXUS-156 is a critical scientific benchmark. It defines the absolute ceiling of the NISQ (Noisy Intermediate-Scale Quantum) era for pharmaceutical research. While we have proven we can understand the origins of life and disease (Projects 01-09) with 156 qubits, the actual design of a quantum cure in silico must await the next generation of hardware.

© 2026 DevSanRafael & Joel Villarroel. Research executed on IBM Fez. Status: Awaiting IBM Hardware Update.